Análisis de las tablas estadísticas en textos escolares y su comprensión por estudiantes de educación básica

Abstract

This doctoral thesis focuses on the analysis of tasks concerning statistical tables in Chilean and Spanish textbooks, as well as the evaluation of how much secondary school pupils in Spain understand the subject. The importance of the topic is justified by the wide use of statistical tables in different fields and the lack of previous research on the subject in the Spanish education. The Ontosemiotic approach to mathematical cognition and instruction is used as a theoretical framework. The investigation is based on the analysis of curriculum documents and on previous research on understanding of statistical tables. Considering these foundations this research has carried out the following stages. Firstly, the presence of statistical tables in the curricular guidelines of Chile and Spain is analysed. In addition, two samples of textbooks from both countries are analysed. The Chilean sample consists of 12 school textbooks from 5th to 8th grade (10-13 years old), and the Spanish sample consists of 24 textbooks from the last years of Primary Education (5th and 6th grades) and all Compulsory Secondary Education. A semiotic analysis of the statistical tables in the texts is carried out identifying the primary mathematical objects defined in the Ontosemiotic Approach, as well as other variables that affect the understanding of this object. In addition, some potential semiotic conflicts are identified. This analysis is the base for determining the semantic definition of the questionnaire to evaluate students' understanding of this topic. Secondly, we designed and validated a questionnaire, based on the semantic definition performed in the previous stage, to assess the understanding of statistical tables with Spanish pupils of 1st and 3rd grades of Compulsory Secondary Education (ESO). The questionnaire items were selected and validated through expert judgement. Lastly, the questionnaire about the understanding of the statistical tables was applied to a sample of 277 Spanish pupils of 1st and 3rd grades of Compulsory Secondary Education, who attended to two public schools in the Autonomous Community of Andalusia. Based on their answers, mathematical knowledge is analyzed, identifying and classifying its main semiotic conflicts. The main contributions of this work are, on the one hand, to provide detailed information on the institutional meaning of reference in textbooks and curriculum guidelines. On the other hand, information is provided on the personal meaning attributed to the statistical tables by the pupils. It also gives information related to the psychometric characteristics of the instrument, which could be applied in other contexts. Finally, the publications derived from the thesis are other contributions that are also included in this report.